Advertisements
Advertisements
प्रश्न
Choose the correct option from the given alternatives:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of
विकल्प
`("d"^2"y")/"dx"^2 + "yx" + ("dy"/"dx")^2 = 0`
`"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`
`"y" ("d"^2"y")/"dx"^2 + 2 ("dy"/"dx")^2 + "y" = 0`
`"xy" "dy"/"dx" + "y" ("d"^2"y")/"dx"^2 = 0`
Advertisements
उत्तर
`"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`
Hint:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` .....(1)
∴ `1/"a"^2 xx "2x" - 1/"b"^2 xx "2y" "dy"/"dx" = 0`
∴ `"x"/"a"^2 - "y"/"b"^2 "dy"/"dx" = 0` ....(2)
and `1/"a"^2 xx 1 - 1/"b"^2 ["y" ("d"^2"y")/"dx"^2 + ("dy"/"dx")^2] = 0` ....(3)
Equations (1), (2) and (3) are consistent
∴ `|("x"^2, - "y"^2, 1),("x", -"y" "dy"/"dx", 0),(1, -["y" ("d"^2"y")/"dx"^2 + ("dy"/"dx")^2], 0)| = 0`
∴ `"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`
APPEARS IN
संबंधित प्रश्न
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = A cos (log x) + B sin (log x)
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
(y - a)2 = 4(x - b)
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
c1x3 + c2y2 = 5
Find the differential equation all parabolas having a length of latus rectum 4a and axis is parallel to the axis.
Find the differential equation of all circles having radius 9 and centre at point (h, k).
Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.
Form the differential equation of all parabolas whose axis is the X-axis.
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = e-x + Ax + B; `"e"^"x" ("d"^2"y")/"dx"^2 = 1`
In the following example verify that the given expression is a solution of the corresponding differential equation:
y = `"a" + "b"/"x"; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" = 0`
Solve the following differential equation:
`"sec"^2 "x" * "tan y" "dx" + "sec"^2 "y" * "tan x" "dy" = 0`
For the following differential equation find the particular solution satisfying the given condition:
`(e^y + 1) cos x + e^y sin x. dy/dx = 0, "when" x = pi/6,` y = 0
For the following differential equation find the particular solution satisfying the given condition:
`("x" + 1) "dy"/"dx" - 1 = 2"e"^-"y" , "y" = 0`, when x = 1
For the following differential equation find the particular solution satisfying the given condition:
`cos("dy"/"dx") = "a", "a" ∈ "R", "y"(0) = 2`
Reduce the following differential equation to the variable separable form and hence solve:
`"dy"/"dx" = cos("x + y")`
Reduce the following differential equation to the variable separable form and hence solve:
`"x + y""dy"/"dx" = sec("x"^2 + "y"^2)`
Solve the following differential equation:
(x2 + y2)dx - 2xy dy = 0
Choose the correct option from the given alternatives:
The solution of `("x + y")^2 "dy"/"dx" = 1` is
The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.
The particular solution of `dy/dx = xe^(y - x)`, when x = y = 0 is ______.
In the following example verify that the given function is a solution of the differential equation.
`"x"^2 + "y"^2 = "r"^2; "x" "dy"/"dx" + "r" sqrt(1 + ("dy"/"dx")^2) = "y"`
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
(y - a)2 = b(x + 4)
Solve the following differential equation:
`"dy"/"dx" = "x"^2"y" + "y"`
Solve the following differential equation:
y log y = (log y2 - x) `"dy"/"dx"`
Find the particular solution of the following differential equation:
`"dy"/"dx" - 3"y" cot "x" = sin "2x"`, when `"y"(pi/2) = 2`
Find the particular solution of the following differential equation:
(x + y)dy + (x - y)dx = 0; when x = 1 = y
The general solution of `(dy)/(dx)` = e−x is ______.
Select and write the correct alternative from the given option for the question
The solution of `("d"y)/("d"x)` = 1 is
Find the differential equation of family of lines making equal intercepts on coordinate axes
Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
The family of curves y = `e^("a" sin x)`, where a is an arbitrary constant, is represented by the differential equation.
Form the differential equation of all straight lines touching the circle x2 + y2 = r2
Find the differential equation of the family of circles passing through the origin and having their centres on the x-axis
Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to the x-axis
Find the differential equation of the family of parabolas with vertex at (0, –1) and having axis along the y-axis
Find the differential equations of the family of all the ellipses having foci on the y-axis and centre at the origin
Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be –8x, where A and B are arbitrary constants
The general solution of the differential equation of all circles having centre at A(- 1, 2) is ______.
Form the differential equation of all lines which makes intercept 3 on x-axis.
The differential equation of all circles passing through the origin and having their centres on the X-axis is ______.
The differential equation for a2y = log x + b, is ______.
Form the differential equation whose general solution is y = a cos 2x + b sin 2x.
Form the differential equation of all concentric circles having centre at the origin.
